基于贝叶斯公式的地下水污染源及含水层参数同步反演

Synchronous inversion of groundwater pollution source and aquifer parameters based on Bayesian formula

针对非均质地下含水层污染源识别及含水层参数反演过程中监测方案优化问题,提出一种基于贝叶斯公式及信息熵最小的累进加井的多井监测方案优化方法.首先,构建假想案例下的二维非均质各向同性潜水含水层水流及溶质运移模型,运用GMS软件进行数值模拟求解.采用最优拉丁超立方抽样方法和Kriging法建立数值模拟模型的替代模型.然后以参数后验分布的信息熵最小为目标函数,采用累进加井的方式进行多井监测方案优化设计.最后根据优化后的监测方案,采用差分进化自适应Metropolis算法进行污染源及含水层参数的同步反演.算例研究表明:在兼顾反演精度及监测成本,并保证每个参数分区内至少有1眼监测井的条件下,5眼井组合监测方案(6,5,1,2,8)为最优监测方案.与信息熵最小的10眼井组合监测方案(1,2,3,4,5,6,7,8,9,10)的参数反演结果相比,5眼井组合监测方案对11个参数α=(X S,Y S,T 1,T 2,Q S,K 1,K 2,K 3,DL 1,DL 2,DL 3)的后验均值偏离率的平均值虽增大1.2%,但监测成本却是10眼井组合监测方案的50%.

Aiming at the optimization of monitoring schemes in the process of the identification of pollution source and the inversion of aquifer parameters in the heterogeneous underground aquifer,this paper proposes an optimization method for the multi-well monitoring schemes based on Bayesian formula and progressive addition of wells with minimum information entropy.Firstly,the two-dimensional heterogeneous isotropic subsurface groundwater flow and solute transport models under hypothetical case were constructed,and the numerical simulation models were solved by GMS software.The surrogate model of the numerical simulation model was established by the optimal Latin hypercube sampling method and Kriging method.Then Taking the minimum information entropy of the parameter posterior distribution as the objective function,the optimization design of multi-well monitoring schemes was carried out by means of progressive addition of wells.Finally,the differential evolution adaptive Metropolis algorithm was used to inverse the pollution source and aquifer parameters synchronously according to the optimized monitoring scheme.The case study results showed that:The 5combination monitoring scheme(6,5,1,2,8)under the condition of taking into account the inversion accuracy and monitoring cost and ensuring that there was at least one monitoring well in each parameter section was the optimal monitoring scheme.Compared with the 10combined monitoring scheme(1,2,3,4,5,6,7,8,9,10)with the smallest information entropy,the 11parameters posterior mean deviation rate increased by 1.2%,but the monitoring cost was reduced by 50%.